Transition to sub-Planck structures through the superposition of q-oscillator stationary states

Abstract

We investigate the superposition of four different quantum states based on the q-oscillator. These quantum states are expressed by means of Rogers-Szego polynomials. We show that such a superposition has the properties of the quantum harmonic oscillator when q -> 1, and those of a compass state with the appearance of chessboard-type interference patterns when q -> 0